We represent an error \({\mathbf {e}}\in \mathrm {SE(3)}\)  as a vector \({\mathbf {\xi }}\in \mathfrak {se}(3)\)  member of the Lie algebra [1]}, [2]}
\({\mathbf {\xi }}^{\wedge } =\begin{bmatrix}{\mathbf {\rho }}\\{\mathbf {\phi }}\end{bmatrix}^{\wedge }=\ \begin{bmatrix}{\mathbf {\phi }}^{\wedge } & {\mathbf {\rho }}\\\mathbf {0}^\mathsf {T} & 0\end{bmatrix}\) 
